endmembers

Endmember is a term used in geology, mineralogy, and remote sensing to denote a pure component at the end of a compositional spectrum. In mineralogy and petrology, endmembers are hypothetical pure compounds that represent the endpoints of a solid solution series (for example, albite and anorthite). In hyperspectral imaging and spectroscopy, endmembers are the observed spectral signatures of distinct materials that can be combined to model mixed observations.

In spectral unmixing, the measured spectrum of a pixel is modeled as a linear or nonlinear mixture of endmember spectra with corresponding abundances. In the linear mixing model, the pixel spectrum equals the sum of endmember spectra weighted by nonnegative abundances that sum to one. The endmembers should be representative of the materials present; they can be obtained from field measurements, laboratory spectra, or spectral libraries.

Extraction and identification of endmembers can be done algorithmically from imagery using methods such as the Pixel Purity Index or the N-FINDR algorithm, as well as through optimization or clustering approaches. In practice, variability in endmember spectra due to lighting, grain size, moisture, and other factors is addressed by using libraries or multiple endmember variants, as in MESMA (Multiple Endmember Spectral Mixture Analysis).

In geology, endmembers define the composition of a solid solution; e.g., plagioclase endmembers albite (NaAlSi3O8) and anorthite (CaAl2Si2O8); pyroxene endmembers enstatite and ferrosilite; garnet endmembers pyrope and almandine.

Limitations include the potential for nonlinear mixing, intimate mixing, spectral variability, and environmental effects, all of which influence endmember selection and unmixing accuracy.